Consider the parametric curve: x = 49 -t^2 y = t^3 - 9t At which t value(s) is t

Question

Consider the parametric curve: x = 49 -t^2 y = t^3 - 9t At which t value(s) is the tangent to this curve vertical? (Note: If there is more than one write them as a comma separated list) t = Write the point(s) at which the tangent is vertical.(Note: If there is more than one write them as a comma separated list, e.g. (1.2), (3.4)) At which t value(s) is the tangent to this curve horizontal? (Note: If there is more than one write them as a comma separated list). t = Write the point(s) at which the tangent is horizontal.(Note: If there is more than one write them as a comma separated list, e.g. (1, 2), (3, 4)) Use a graphing device to graph the curve and check your work.

Explanation / Answer

given x = 49-t2

y = t3-9t

a) for vertical tangent dx/dt=0

dx/dt = -2t = 0

t = 0

b) points are (49,0)

c) for harinzantal tangent dy/dt=0

dy/dt = 3t2 - 9 = 0

t2 - 9 =0

t2 = 9

t = +/- 3

d) points are (40,0),(40,0)

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